Modern Theory of the Atom:
Quantum Mechanical Model
Recap of Bohr Model
electrons:
particles moving in circular orbits with specific speed, position, & energy
energy levels possess specific quantum of energy
electrons can move between energy levels
higher energy levels farther from nucleus
• e- moving up to higher E level: electron absorbs energy
• e- moving down to lower E level: electron emits light energy
ground state:
electrons located in lowest possible energy levels, closest can be to
nucleus
DeBroglie Electron-Wave
Proposed this Idea: if light can show both particle and
wave behavior, maybe matter can too
wavelength describing
electron depends on energy
of electron
at certain energies,
electron waves make
standing waves in atom
wave does not represent
path of electron
2 kinds of waves
Traveling Wave
• wave not confined to
given space
Standing Wave
• confined to given space
(ends are pinned)
• travels from one
location to another
• interference between
incident & reflected
waves
• interrupted by hitting
boundary or another
wave
• at certain frequencies:
– certain points seem to be
standing still
– other points - displacement
changes in regular way
Transverse (ocean)
Longitudinal (compressed/sound)
Bohr Model vs. Modern Theory
•
•
•
•
•
electron = particle
e- path is orbit
holds 2n2 electrons
circular path
each orbit has
specific energy
• can find exact
position/ speed
•
•
•
•
•
electron = wave
e– path is orbital
holds 2 electrons
not necessarily circular
each orbit has
specific energy
• probable location
Heisenberg uncertainty principle
• fundamentally impossible to know velocity
& position of particle at same time
• impossible to make observation without
influencing system
• cannot specify both position & speed of
electron
– can only determine probability of electron’s
location in given region of space
Orbital – Modern Theory
• orbital: term describes region where e- might
be found
• each orbital:
– specific energy & specific shape
– described by 4 parameters of wave function (like
an address)
• quantum numbers = n, l, m, s
• structure of orbitals explain:
– bonding, magnetism, atom size, crystal structure
n: principal quantum number
• specifies atom’s principal energy levels
• whole number values: 1, 2, 3, 4, …
• 2n2 = maximum # electrons in any principal
energy level
l = describes sublevels
• sublevels are labelled by shape:
–s, p, d, f
s orbitals:
spherical
p orbitals: dumbbell shaped
d orbitals: complex shapes
f orbitals: complex shapes too
Sublevels
1st principal energy level:
s (1 sublevel)
2nd level:
s,p (2 sublevels)
3rd level:
s,p,d (3 sublevels)
4th level:
s,p,d,f (4 sublevels)
m = 3rd quantum number (orbitals)
• each sublevel contains 1 or more orbitals
• each orbital holds a max of 2 electrons
•
•
•
•
s has 1 orbital
p has 3 orbitals
d has 5 orbitals
f has 7 orbitals
2 electrons)
1st PEL =s (1 sublevel) = 1 orbital (__
2nd PEL =s,p (2 sublevels) = 4 orbitals (__8 e-)
3rd PEL = s,p,d (3 sublevels) = 9 orbitals (___
18 e-)
32 e-)
4th PEL s,p,d,f (4 sublevels) = 16 orbitals (___
4th quantum number = s
• e- spin: 2 possible values
– clockwise and counter clockwise
– Illustrated by arrows with opposite directions

address for each electron
• 4 quantum numbers
• no 2 e- can
– occupy the same space in atom
– can have same 4 quantum numbers
therefore only 2 electrons per orbital
(Pauli exclusion principle)
Memorize
s
p
d
f
1
3
5
7
2e- 6e10e-
s
p
d
f
sublevels
# of orbitals
14e-
max # of electrons
*each orbital holds 2 e-
electron configurations
• add e- to atoms so that eare in lowest energy levels –
most stable or ground state
configuration
• start with 1s, then work
upward in order of
increasing energy
• use Aufbau rule.
3rd principal energy
level, 3 sublevels
2nd principal energy level, 2 sublevels –
s&p

1st principal energy level, 1 sublevel – s
Each box represents an orbital and holds 2 electrons
Aufbau Principle
1s
2s
3s
4s
5s
6s
7s
follow arrows
2p
3p
4p
5p
6p
7p
3d
4d
5d
6d
7d
4f
5f
6f
7f
sequence of orbitals:
1s, 2s, 2p, 3s, 3p, 4s,
3d, 4p, 5s, 4d, …
exceptions do occur:
- half-filled orbitals
have extra stability
- magic # is 8
1s2
2s2 2p6
3s2 3p6 3d10
4s2 4p6 4d10 4f14
5s2 5p6 5d10 5f14
6s2 6p6 6d10
7s2 7p6 7d10
He
1s2
C
1s22s22p2
22s22p63s2
1s
Mg
Zn
1s22s22p63s23p6 4s23d10
from these modern configurations, we can figure out Bohr Configurations
All you have to do is add up the electrons in each shell (energy level)
He 1s
2
1=2
2
C
1s22s22p2
1=2
2 = 2+2
2–4
Mg
Zn
1s22s22p63s2
1=2
2 = 2+6
3=2
2–8–2
1s22s22p63s23p64s23d10
1 = 2 2 = 2+6 3 = 2+6+10
2 – 8 – 18 – 2
4=2
Hund’s Rule
• most e- with same spin, so if more than
one same orbital:
e- fill orbitals one at time before pairing up
• 1s2
2s2
2p4
Which element? Boron
How many unpaired e-? 1
How many principal energy level’s occupied?
How many principal energy level’s are fully
occupied? 1
How many sublevels contain e-? 3
How many sublevels full? 2
How many orbitals contain e-?
3
2